Given: {(3-x)(2x+4)}^½ This expression is also written in a radical form: √{(3-x)(2x+4)}
Domain,R, is a term that descibes the set of values, x∊R, for which a function of x, f(x) is defined.
Let f(x)=√{(3-x)(2x+4)} and g(x)=(3-x)(2x+4), so f(x)=√g(x). Thus, the condition that defines the real values of f(x) is: g(x)≥0 We have: (3-x)(2x+4)≥0
The coefficient of x² in g(x) is negative(-2), so the graph of g(x) is convex upwards and intercepts x-axis(y=0) at x=-2 and x=3. And (3-x)(2x+4)≥0, so the domain of x is: -2≤ x ≥3.
Therefore, the largest value of domain is: x=3